Question: What's the first wrong statement in the proof below that $ \triangle BCA \cong \triangle BCE$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \angle BED \cong \angle BAC$ $, \ $ $ \overline{DE} \cong \overline{AC}$ $, \ $ $ \angle BDE \cong \angle ACB$ $, \ $ $ \overline{CF} \cong \overline{BC}$ $, \ $ $ \angle CFE \cong \angle ABC$ $, \ $ and $\ $ $ \overline{EF} \cong \overline{AB}$ Proof $ \triangle BCA \cong \triangle BDE$ because ASA $ \overline{AB} \cong \overline{BE}$ because corresponding parts of congruent triangles are congruent $ \angle CFE \cong \angle ACB$ because corresponding parts of congruent triangles are congruent $ \triangle FCE \cong \triangle BCA$ because SAS $ \angle CEF \cong \angle BAC$ because corresponding parts of congruent triangles are congruent $ \triangle BCA \cong \triangle BCE$ because SSS
Solution: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \angle ACB \cong \angle CFE$ is the first wrong statement.